"... Summary. A twisted vector-bundle approach to α-induction and modular invari-ants. 1 Introduction and statement of results The Verlinde algebra is central to conformal field theory and consequently also to the braided subfactor approach to modular invariants. In the braided sub-factor approach to mod ..."

Summary. A twisted vector-bundle approach to α-induction and modular invari-ants. 1 Introduction and statement of results The Verlinde algebra is central to conformal field theory and consequently also to the braided subfactor approach to modular invariants. In the braided sub-factor approach to modular invariants one has first a factor N, which we can take to be type III, and a non-degenerately braided system of endomorphisms

"... Abstract. The E6 state sum invariant is a topological invariant of closed 3-manifolds constructed by using the 6j-symbols of the E6 subfactor. In this paper, we introduce the E6 linear skein as a certain vector space motivated by E6 subfactor planar algebra, and develop its linear skein theory by sh ..."

Abstract. The E6 state sum invariant is a topological invariant of closed 3-manifolds constructed by using the 6j-symbols of the E6 subfactor. In this paper, we introduce the E6 linear skein as a certain vector space motivated by E6 subfactor planar algebra, and develop its linear skein theory by showing many relations in it. By using this linear skein, we give an elementary self-contained construction of the E6 state sum invariant. 1.

...Properties and examples of our state sum invariant The values of the E6 state-sum invariant have been calculated for the lens space L(p; q) for q = 1; 2; 3 in [SuW], and for some other 3-manifolds in =-=[SaW]-=-. In this section, we calculate the values of the E6 state-sum invariant for the lens spaces L(4; 1), L(5; 2) and L(5; 1) in terms of our E6 linear skein in Examples 7.5, 7.6 and 7.7. Further, we revi...

"... 1. The scope of this review 2. Terms, definitions, models and measures 3. An overview of the evidence of culture’s contribution to regeneration 4. Evidence-based case studies of culture’s contribution to regeneration ..."

1. The scope of this review 2. Terms, definitions, models and measures 3. An overview of the evidence of culture’s contribution to regeneration 4. Evidence-based case studies of culture’s contribution to regeneration

...rup subfactor comes from the following fact that the 3-sphere S3 and the Poincaré homology 3-sphere Σ(2, 3, 5) are distinguished by the Turaev-Viro-Ocneanu invariant from the Haagerup subfactor (see =-=[SW]-=-). On the other hand, there is a hierarchy of understanding: (1) conformal field theory, (2) statistical mechanical models, (3) subfactors, vertex operator algebras and twisted K-theory, (4) modular t...